Questions: 3/4(-8v-4)=2(v+6)-3v

Transcript text: $\frac{3}{4}(-8 v-4)=2(v+6)-3 v$

Solution

Solution Steps

To solve the equation $\frac{3}{4}(-8v - 4) = 2(v + 6) - 3v$, we need to follow these steps:

Distribute the $\frac{3}{4}$ on the left-hand side.
Simplify both sides of the equation.
Combine like terms.
Solve for $v$.

Step 1: Distribute and Simplify

First, distribute $\frac{3}{4}$ on the left-hand side of the equation: \[ \frac{3}{4}(-8v - 4) = -6v - 3 \] The equation becomes: \[ -6v - 3 = 2(v + 6) - 3v \]

Step 2: Simplify the Right-Hand Side

Next, simplify the right-hand side of the equation: \[ 2(v + 6) - 3v = 2v + 12 - 3v = 12 - v \] So the equation now is: \[ -6v - 3 = 12 - v \]

Step 3: Combine Like Terms

Combine like terms to isolate $v$: \[ -6v + v = 12 + 3 \] \[ -5v = 15 \]

Step 4: Solve for $v$

Solve for $v$ by dividing both sides by $-5$: \[ v = \frac{15}{-5} = -3 \]

Final Answer

$\boxed{v = -3}$

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